A mathematical model of symmetry based on mathematical definition |
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| Authors: | Liu Yusheng Yang Jiangxin Wu Zhaotong Gao Shuming |
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| Institution: | (1) State Key Laboratory of CAD&CG, Zhejiang University, 310027 Hangzhou, China;(2) Institute of Production Engineering, Zhejiang University, 310027 Hangzhou, China |
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| Abstract: | Tolerance is imperative for seamless integration of CAD/CAM (Computer Aided Disign/Computer Aided Manufacture) which is just
a text attribute and has no semantics in present CAD systems. There are many tolerance types, the relations between which
are very complicated. In addition, the different principles of tolerance make study of tolerance difficult; and there may
be various meanings or interpretation for the same type of tolerance because of the literal definition. In this work, latest
unambiguous mathematical definition was applied to study, explain and clarfy: (1) the formation and representation of tolerance
zone, and (2) the formation and representation of variational elements; after which, the mathematical models of symmetry of
different tolerance principles and different interpretations were derived. An example is given to illustrate the application
of these models in tolerance analysis.
Project supported by the National Natural Science Foundation of China for Innovation Research Groups(No.60021201) and NSFC(Nos.59705022
& 69973045). |
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| Keywords: | mathematical definition symmetry tolerance mathematical model CAD/CAM production engineering |
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